Jake begins the summer with 1,000 marbles in his collection. He aims to have a minimum of 500 marbles left by the end of the summer. Each week, he gives away 100 marbles to friends. Write an inequality to determine the number of weeks Jake can continue giving away marbles and find the solution.(1 point)
Responses
1000−100w≥500; w≥51000−100w≥500; w≥5
1000−100w≥500; w≤51000−100w≥500; w≤5
1000−100w≤500; w≥61000−100w≤500; w≥6
1000+100w≥500; w≥6
1000 - 100w ≥ 500; w ≥ 5
proof
To prove that the solution is w ≥ 5, we can substitute the value of w into the original inequality and evaluate it.
Substituting w = 5 into the inequality 1000 - 100w ≥ 500, we get:
1000 - 100(5) ≥ 500
1000 - 500 ≥ 500
500 ≥ 500
Since 500 is greater than or equal to 500, the inequality is true.
Now, let's test a value less than 5.
Substituting w = 4 into the inequality 1000 - 100w ≥ 500, we get:
1000 - 100(4) ≥ 500
1000 - 400 ≥ 500
600 ≥ 500
Since 600 is greater than or equal to 500, the inequality is also true.
Therefore, any value of w that is greater than or equal to 5 will make the inequality true.
Hence, the solution is w ≥ 5.
Mark runs a stall selling handmade cards and bookmarks.
Each handmade card costs $20.00.
Each bookmark costs $2.50.
Mark wants his total sales to reach a minimum of $90.00 through the sale of at least one handmade card and several bookmarks. What inequality represents the various quantities of bookmarks (x) Mark must sell?
To represent the various quantities of bookmarks (x) Mark must sell, we can use the inequality:
2.50x + 20.00 ≥ 90.00